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Pump Affinity Law: Power vs Speed

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}
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Worked example: 15 kW at 1450 rpm slowed to 1160 rpm → 7680 W. Press Try an example to run it live, then adjust anything.

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Pump Efficiency from Hydraulic and Shaft Power
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See also

Fan Affinity Law: Power vs Speed: Both use shaft power and shaft speed.Fan Affinity Law: Airflow vs Speed: Both use shaft speed.Fan Affinity Law: Static Pressure vs Speed: Both use shaft speed.Fan Brake Horsepower: Both use shaft power.Pump Affinity Law: Flow vs Speed: Both use shaft speed.Pump Affinity Law: Head vs Speed: Both use shaft speed.
4 more relatedPump Brake Horsepower: Both use shaft power.Pump Efficiency from Hydraulic and Shaft Power: Both use shaft power.Pump Specific Speed (Ns): Both use shaft speed.Steam Turbine Power Output: Both use shaft power.
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Pump Affinity Law: Power vs Speed explained

N2N1P1P2

Power is head times flow, and head already carries a square, so power rides the cube of speed. Slow a 15 kW pump from 1450 to 1160 rpm, a mere 20% cut, and it draws 15 × 0.8³ = 7.68 kW, a 49% saving. That cube is why throttling a valve to reduce flow is such a waste: the pump still spins at full speed burning full power while you dissipate the surplus as heat and noise across the valve seat.

Two cautions temper the arithmetic. Real pump and motor efficiency sags at part speed, so the field saving is nearer 45% than 49%, and any static lift in the system means the pump cannot follow the cubic curve all the way down. Chilled-water plants still routinely bank 40–60% on pumping energy, which is why ASHRAE 90.1 has effectively mandated variable-speed pumping on larger variable-flow systems.

Pump Affinity Law: Power vs Speed formula

P2P1=(N2N1)3\frac{P_2}{P_1} = \left(\frac{N_2}{N_1}\right)^{3}
Where
  • P1P_1= Power at speed 1 (W)
  • N1N_1= Speed 1 (rpm)
  • P2P_2= Power at speed 2 (W)
  • N2N_2= Speed 2 (rpm)
In this toolkit

The pump and fan affinity laws

7 formulasHow flow, head and power scale with impeller speed and diameter — the first, second and third power relationships behind every VFD retrofit.

Revised 16 October 2026
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formula.expert. (2026, October 16). Pump Affinity Law: Power vs Speed Formula & Calculator. https://formula.expert/solvers/pump-affinity-power-speed

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